The potential gradients on the potentiometer wire are V₁ and V₂ with an ideal cell and a real cell of same emf in the primary circuit then

Potential gradient is the drop in potential in the wire per unit length. 

Potential drop across the wire is 

$\mathrm{V} = \mathrm{E}-\mathrm{ir}$ where r is the internal resistance.

Potential gradient $\mathrm{k} = \frac{\mathrm{V}}{\mathrm{L}}=\frac{\mathrm{E}-\mathrm{ir}}{\mathrm{L}}$

r = 0 for ideal cell. 

${\mathrm{V}}_1=\frac{\mathrm{E}}{\mathrm{L}} \& {\mathrm{V}}_2=\frac{\mathrm{E}-\mathrm{ir}}{\mathrm{L}}$

Therefore, V₁ > V2